Site-mixing model

Stoesell, R.K. (1984) Regular solution site-mixing model for chlorites. Clays Clay Minerals, 32, 205-212. 

Figure 539 Intracrystalline distribution of Fe +-Mg + between Y(Ml, M2, M3) and M4 sites in natural cummingtonites. (A) Regular site-mixing model. (B) Ideal site-mixing model. (C) Arrhenius plot of equilibrium constant.

It is important to emphasize here that, theoretically, if a solid mixture is ideal, intracrystalline distribution is completely random (cf section 3.8.1) and, in these conditions, the intracrystalline distribution constant is always 1 and coincides with the equilibrium constant. If the mixture is nonideal, we may observe some ordering on sites, but intracrystalline distribution may still be described without site interaction parameters. We have seen in section 5.5.4, for instance, that the distribution of Fe and Mg on Ml and M3 sites of riebeckite-glaucophane amphiboles may be approached by an ideal site mixing model—i.e.. 

For the calculation of solid-solution mineral behavior, two conceptual models may be used the end-member model (arbitrary mixing of two or more phases) and the site-mixing model (substituting elements can replace certain elements only at certain sites within the crystal structure). 

In the version 7.2 of the program EQ 3/6, the modeling of solid-solution minerals using end-member and site-mixing models (chapter 1.1.4.1.3) had been already realized compared to the PHREEQC version from 1995. Table 20 represents the solid-solution minerals that are considered in Gemboch s data set of EQ 3/6. Using the concept of solid-solution minerals, surface complexation can be modeled as well. 

Table 5.40 Binary interaction parameters for pyroxenes. Parameters refer to an ionic mixing model in which n is the number of sites over which permutability is calculated—i.e., Gmixing = tiRT (Xi In Xj + X2 In X2). Data in J/mole (H), J/(mole X K) (5), and J/(bar X mole) (V), respectively.

Model Fitting to Mixing-Cell Data Multiple-site kinetic models have been used to describe pesticide and herbicide movement in soils (15,16,17), cesium migration in columns (18), and strontium migration in a sandy aquifer over a twenty-year time period (1L). The results of the selective extraction procedures in all experiments discussed here suggest that a multi-site model should provide a better fit of the data than a single-site model. This hypothesis is supported by the variances in Table I, with the possible exception of selenium. 

Another mixed model, called here Site-Property analysis (SP analysis), can be obtained [Authors, this book] it represents information regarding the presence of each substituent group in each site by the corresponding physico-chemical properties, i.e. the information of the indicator variables I, of the Fujita-Ban analysis is preserved in each site but is represented by the set of selected properties ... 

Mixing intra- and intermolecular connections The extended site-binding model... 

Statistical modeling of pentad distributions of polypropenes prepared with these catalyst systems can be satisfactorily done using a two-site modeF - based on a mixing of a chain-end-controlled site (to model the atactic blocks) and an enantiomorphic site (for isotactic blocks). ... 

The site-distribution model has recently been extended to mixed-gas sorption, and is able to account for competitive sorption effects (88). As with the dualmode model, the site-distribution model allows for the prediction of mixed-gas sorption by using parameters obtained from experimentally less complicated pure-gas sorption measurements. Like the dual-mode model, the site-distribution model is phenomenological, while the dual-mode model uses the bulk specific volume Vg and extrapolated equilibrium volume Ve as key parameters the site-distribution model relies upon the bulk shear modulus /u.g as a key parameter. The use of bulk parameters to characterize sorption which occurs at the atomistic scale is questionable from a fundamental point of view nevertheless, such models provide useful tools to describe and even predict the effect of conditioning and physical aging... 

It is critical, therefore, to establish a site-relevant isotopic baseline for interpreting human skeletal data. Analyses of faunal remains provide a good estimate both of the animals themselves and the plants they consume. This is particularly important since in many areas while maize may be the only C4 plant cultivated and consumed directly by humans, other C4 grasses may exist and be consumed by grazing herbivores which pass on an enriched isotopic signature to their human consumers. Information from ethnohistoric and other sources, along with isotopic data for relevant food resources, may then be used to propose specific dietary mixing models to account for human bone isotope ratios (27). 

---